Density

Density is a comparison of mass and volume. In other words, density relates two types of units, mass and volume.

For example, water has a density of 1 g/ml. This means that 1 milliliter of water has a mass of 1 gram. This is a density that you need to memorize, but, given enough information, the density of other materials can be calculated. For example, in the following problem the density of a box is asked for. Note that I am showing you how to think through such a problem.

Problem

The density of a box, which is 2.0 m long, 0.5 m wide, and 1.3 m high and has a mass of 300.0 kg is  ? kg/m³

Facts:

Equations You should know:

d = m/v     (density = mass/volume ; density equal mass divided by volume)

v = l x w x h  (volume equals length times width time height)

Information from the problem:

v = 2.o m x 0.5 m x 1.3 m

= 1.3 m^{3   (Note: m x m x m = cubed meters)}

mass box = 300.0 kg

Problem Map (This is a basic plan starting with facts from the problem and ending with units that are to be in the answer.)

START——————————————————> Finish

mass and volume  are given ——————————–> density  = ? kg/m³

Clue: If you are trying to calculate the density of something, USE THE DENSITY EQUATION

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d = m/v = 300.0 kg/1.3 m³

^{= 230.769} kg/1m³

Significant Figures: Your answer can only be accurate to the least number of significant figures in the problem.

2.0  = 2 sig figs

1.3 =  2 sig figs

300.0 = 4 sig figs

Answer: 230 kg/m³ (two sig figs)